Solve the following
Question:

The reaction $2 X \rightarrow B$ is a zeroth order reaction. If the initial concentration of $X$ is $0.2 \mathrm{M}$, the half-life is $6 \mathrm{~h}$. When the initial concentration of $\mathrm{X}$ is $0.5 \mathrm{M}$, the time required to reach its final concentration of $0.2 \mathrm{M}$ will be :

  1. $9.0 \mathrm{~h}$

  2. $12.0 \mathrm{~h}$

  3. $18.0 \mathrm{~h}$

  4. $7.2 \mathrm{~h}$


Correct Option: , 3

Solution:

For the reaction $2 \mathrm{X} \rightarrow \mathrm{B}$, follow zeroth order Rate equation is

$K_{t}=[A]_{0}-[A]$

For the half-life; $\mathrm{t}=\mathrm{t}_{1 / 2}$ and $[\mathrm{A}]=0.1$

$\mathrm{K} \mathrm{t}_{1 / 2}=0.2-0.1$

$\frac{0.2-0.1}{6}=\frac{0.1}{6} \mathrm{Mhr}^{-1}$

$\therefore$ Time required to reach from $0.5 \mathrm{M}$ to $0.2 \mathrm{M}$

$\mathrm{Kt}=[\mathrm{A}]_{0}-[\mathrm{A}]$

$\frac{0.1}{6} \times \mathrm{t}=(0.5-0.2) ; \mathrm{t}=18$ hour

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